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Graphs and Combinatorics

, Volume 35, Issue 1, pp 231–238 | Cite as

Degree Conditions for Graphs to Have Spanning Trees with Few Branch Vertices and Leaves

  • Shun-ichi Maezawa
  • Ryota MatsubaraEmail author
  • Haruhide Matsuda
Original Paper
  • 29 Downloads

Abstract

A leaf of a tree is a vertex of degree one and a branch vertex of a tree is a vertex of degree strictly greater than two. This paper shows two degree conditions for graphs to have spanning trees with total bounded number of branch vertices and leaves. Moreover, the sharpness of our results is shown.

Keywords

Spanning tree Branch vertex Leaf Fan-type degree condition 

Notes

References

  1. 1.
    Broersma, H., Tuinstra, H.: Independence trees and Hamilton cycles. J. Graph. Theory 29, 227–237 (1998)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Nikoghosyan, ZhG: Spanning trees with few branch and end vertices. Math. Probl. Comput. Sci. 46, 18–25 (2016)MathSciNetGoogle Scholar
  3. 3.
    Saito, A., Sano, K.: Spanning trees homeomorphic to a small tree. Discret. Math. 339, 677–681 (2016)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer Japan KK, part of Springer Nature 2019

Authors and Affiliations

  • Shun-ichi Maezawa
    • 1
  • Ryota Matsubara
    • 2
    Email author
  • Haruhide Matsuda
    • 2
  1. 1.Graduate School of Environment and Information SciencesYokohama National UniversityYokohamaJapan
  2. 2.Department of MathematicsShibaura Institute of TechnologySaitamaJapan

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